Question

Find the coordinates of the point 3/10 of the way from a to b. a= (-3, -5) b = (10, 7)

Answer 1

`\displaystyle\\Answer:\ (0,-(29)/(13) )`

Explanation:

`\displaystyle\\A(-3,-5)\ \ \ \ \ B(10,7) \ \ \ \ \ \lambda=3/10=0.3\ \ \ \ \ C(x_C,y_C)=?\\\\\boxed {x_C=(x_A+\lambda x_B)/(1+\lambda) }\ \ \ \ \ \ \ \ \ \ \boxed {y_C=(y_A+\lambda y_B)/(1+\lambda) }\\\\x_C=(-3+0.3(10))/(1+0.3) \\\\x_C=(-3+3)/(1.3) \\\\x_C=(0)/(1.3)\\\\x_C=0\\`

`\displaystyle\\y_C=(-5+0.3(7))/(1+0.3) \\\\y_C=(-5+2.1)/(1.3) \\\\y_C=(-2.9)/(1.3) \\\\y_C=-(2.9(10))/(1.3(10)) \\\\y_C=-(29)/(13)`

`\displaystyle\\Thus,\ C(0,-(29)/(13) )`